수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [정수] 소수일까?

△π 2020.07.11 16:43 조회 626

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

f(n)=n(n+1)+41이 있다고 하자.f(0)부터 f(39)까지는 모두 소수라고 한다.

(1)f(n)은 41보다 작은 소인수를 가질 수 없음을 보여라.

(2)f(n)이 합성수가 되는 연속하는 40개의 n을 찾아라.

(3)f(n)=an+b일 때, 모든 n에 대해서 f(n)이 소수인 f(n)은 없음을 보여라.

(4)f(n)=an²+bn+c일 때, 모든 n에 대해서 f(n)이 소수인 f(n)은 없음을 보여라.

이전글 문제[기출 변형, 대수]

다음글 [창의] 52개의 오이

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